# Non-parametric B-spline decoupling of multivariate functions

arXiv: https://arxiv.org/abs/2504.03263 · HTML: https://mlsanity.com/paper/2504.03263/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Apr 2025.

## Built on by (most cited first, 2 of 2)

- [Robust Basis Spline Decoupling for the Compression of Transformer Models](https://mlsanity.com/paper/2605.18794/) (2026)
- [Making Tensor Decoupling More Robust and Less Parametric](https://mlsanity.com/paper/2610.16937/) (2026)

## Abstract (arXiv)

Many scientific fields and applications require compact representations of multivariate functions. For this problem, decoupling methods are powerful techniques for representing the multivariate functions as a combination of linear transformations and nonlinear univariate functions. This work introduces an efficient decoupling algorithm that leverages the use of B-splines to allow a non-parametric estimation of the decoupling's internal functions. The use of B-splines alleviates the problem of choosing an appropriate basis, as in parametric methods, but still allows an intuitive way to tweak the flexibility of the estimated functions. Besides the non-parametric property, the use of B-spline representations allows for easy integration of nonnegativity or monotonicity constraints on the function shapes, which is not possible for the currently available (non-)parametric decoupling methods. The proposed algorithm is illustrated on synthetic examples that highlight the flexibility of the B-spline representation and the ease with which a monotonicity constraint can be added. The examples also show that if monotonic functions are required, enforcing the constraint is necessary.